Note: Descriptions are shown in the official language in which they were submitted.
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AUXETIC STRUCTURES WITH ANGLED SLOTS IN ENGINEERED PATTERNS
FOR CUSTOMIZED NPR BEHAVIOR AND IMPROVED COOLING
PERFORMANCE
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the right of priority to U.S. Provisional
Patent Application No.
62/118,826, filed on February 20, 2015, and U.S. Provisional Patent
Application No.
62/101,840, filed on January 9, 2015, both of which are incorporated herein by
reference in
their respective entireties.
TECHNICAL FIELD
[0002] The present disclosure relates generally to porous materials and
cellular solids with
tailored isotropic and anisotropic Poisson's ratios. More particularly,
aspects of this
disclosure relate to auxetic structures with engineered patterns that exhibit
negative Poisson's
Ratio (NPR) behavior, as well as systems, methods and devices using such
structures.
BACKGROUND
[0003] When materials are compressed along a particular axis, they are most
commonly
observed to expand in directions transverse to the applied axial load.
Conversely, most
materials contract along a particular axis when a tensile load is applied
along an axis
transverse to the axis of contraction. The material property that
characterizes this behavior is
known as the Poisson's Ratio, which can be defined as the negative of the
ratio of
transverse/lateral strain to axial/longitudinal strain under axial loading
conditions. The
majority of materials are characterized by a positive Poisson's Ratio, which
is approximately
0.5 for rubber, approximately 0.3 for aluminum, brass and steel, and
approximately 0.2 for
glass.
[0004] Materials with a negative Poisson's Ratio (NPR), on the other hand,
will contract (or
expand) in the transverse direction when compressed (or stretched) in the
axial direction.
Materials that exhibit negative Poisson's Ratio behavior are oftentimes
referred to as
"auxetic" materials. The results of many investigations suggest that auxetic
behavior
involves an interplay between the microstructure of the material and its
deformation.
Examples of this are provided by the discovery that metals with a cubic
lattice, natural
layered ceramics, ferroelectric polycrystalline ceramics, and zeolites may all
exhibit negative
Poisson's Ratio behavior. Moreover, several geometries and mechanisms have
been proposed
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to achieve negative values for the Poisson's Ratio, including foams with
reentrant structures,
hierarchical laminates, polymeric and metallic foams. Negative Poisson's Ratio
effects have
also been demonstrated at the micrometer scale using complex materials which
were
fabricated using soft lithography and at the nanoscale with sheet assemblies
of carbon
nanotub es.
[0005] A significant challenge in the fabrication of auxetic materials is that
it usually
involves embedding structures with intricate geometries within a host matrix.
As such, the
manufacturing process has been a bottleneck in the practical development
towards
applications. A structure which forms the basis of many auxetic materials is
that of a cellular
solid. Research into the deformation of these materials is a relatively mature
field with
primary emphasis on the role of buckling phenomena, on load carrying capacity,
and energy
absorption under compressive loading. Very recently, the results of a combined
experimental
and numerical investigation demonstrated that mechanical instabilities in 2D
periodic porous
structures can trigger dramatic transformations of the original geometry.
Specifically,
uniaxial loading of a square array of circular holes in an elastomeric matrix
is found to lead to
a pattern of alternating mutually orthogonal ellipses while the array is under
load. This
results from an elastic instability above a critical value of the applied
strain. The geometric
reorganization observed at the instability is both reversible and repeatable
and it occurs over a
narrow range of the applied load. Moreover, it has been shown that the pattern
transformation leads to unidirectional negative Poisson's Ratio behavior for
the 2D structure,
i.e., it only occurs under compression.
[0006] U.S. Patent No. 5,233,828 ("828 Patent") shows an example of an
engineered void
structure ¨ a combustor liner or "heat shield" ¨ utilized in high temperature
applications.
Combustor liners are typically used in the combustion section of a gas
turbine. Combustor
liners can also be used in the exhaust section or in other sections or
components of the gas
turbine, such as the turbine blades. In operation, combustors burn gas at
intensely high
temperatures, such as around 3,000 F or higher. To prevent this intense heat
from damaging
the combustor before it exits to a turbine, the combustor liner is provided in
the interior of the
combustor to insulate the surrounding engine. To minimize temperature and
pressure
differentials across a combustor liner, cooling feature have conventionally
been provided,
such as is shown in the '828 Patent, in the form of spaced cooling holes
disposed in a
continuous pattern. As another example, U.S. Patent No. 8,066,482 B2 presents
an
engineered structural member having elliptically-shaped cooling holes to
enhance the cooling
of a desired region of a gas turbine while reducing stress levels in and
around the cooling
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holes. European Patent No. EP 0971172 Al likewise shows another example of a
perforated
liner used in a combustion zone of a gas turbine. None of the above patent
documents,
however, provide examples disclosed as exhibiting auxetic behavior or being
engineered to
provide NPR effects.
[0007] U.S. Patent Application Pub. No. 2010/0009120 Al discloses various
transformative
periodic structures which include elastomeric or elasto-plastic periodic
solids that experience
transformation in the structural configuration upon application of a critical
macroscopic stress
or strain. Said transformation alters the geometric pattern, changing the
spacing and the shape
of the features within the transformative periodic structure. Upon removal of
the critical
macroscopic stress or strain, these elastomeric periodic solids recover their
original form. By
way of comparison, U.S. Patent Application Pub. No. 2011/0059291 Al discloses
structured
porous materials, where the porous structure provides a tailored Poisson's
ratio behavior.
These porous structures consist of a pattern of elliptical or elliptical-like
voids in an elastomeric
sheet which is tailored, via the mechanics of the deformation of the voids and
the mechanics of
the deformation of the material, to provide a negative or a zero Poisson's
ratio. All of the
foregoing patent documents are incorporated herein by reference in their
respective entireties
and for all purposes.
SUMMARY
[0008] Aspects of the present disclosure are directed towards auxetic
structures with
repeating patterns of elongated apertures (also referred to herein as "voids"
or "slots") that
are engineered to provide a desired negative Poisson's Ratio (NPR) behavior
and improved
cooling performance. Unlike prior art NPR void shapes that extend through the
plane of the
structure material, traversing the thickness of the material in a direction
normal to the
material's plane, NPR voids disclosed herein traverse the thickness of the
material at an angle
that is oblique to the materials' plane. These angled void configurations
enhance the cooling
performance of the structure while retaining a low porosity and providing a
desired NPR
behavior. Other aspects of the present disclosure are directed to multi-
functional NPR
structures with angled air passages in the hot section of a gas turbine.
Additional aspects are
directed towards gas turbine combustors that are made with walls from a
material with
engineered angled void features that provide particular thermal, damping
and/or acoustic
functionalities. Such functionalities include, for example, acoustic
attenuation (or noise
damping), stress reduction (or load damping), and thermal cooling (or heat
damping).
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[0009] According to aspects of the present disclosure, auxetic structures with
angled NPR
slots are disclosed. In an example, an auxetic structure includes an
elastically rigid body,
such as a metallic sheet or other sufficiently elastic solid material, with
opposing top and
bottom surfaces. First and second pluralities of elongated apertures extend
through the
elastically rigid body from the top surface to the bottom surface. The first
plurality of
elongated apertures extends transversely (e.g., orthogonally) with respect to
the second
plurality of elongated apertures. The first and/or second pluralities of
elongated apertures are
obliquely angled with the top and/or bottom surfaces of the elastically rigid
body. In an
example, each slot traverses the thickness of a sheet material at an angle
that is oblique (e.g.,
approximately 40-70 degrees) to the material's plane. The elongated apertures
are
cooperatively configured to provide a desired or minimum cooling performance
while
exhibiting stress reduction through negative Poisson's Ratio (NPR) behavior
under
macroscopic planar loading conditions. By way of example, the elongated
apertures are
engineered with a predefined porosity, a predetermined pattern, and/or a
predetermined
aspect ratio to achieve the desired NPR behavior. The auxetic structure may
exhibit an
effusion cooling effectiveness of approximately 30-50%, a porosity of about
0.3 to about 9%,
and a Poisson's Ratio of approximately -0.2 to -0.9%. Cooling effectiveness
(Eta) can be
defined as the difference of the hot gas temperature to the wall temperature
in the presence of
a cooling device divided by the difference of the hot gas temperature to the
temperature of the
supplied cooling gas: Eta=(T hotgas-T wall)/(T hotgas-T coolant).
[0010] In accordance with other aspects of this disclosure, effusion-cooling
auxetic sheet
structures are featured. In an example, an effusion-cooling auxetic sheet
structure is presented
which includes a metallic sheet with opposing top and bottom surfaces. First
and second
pluralities of elongated apertures extend through the metallic sheet from the
top surface to the
bottom surface. The first plurality of elongated apertures has a first set of
geometric
characteristics and is arranged in a first pattern. Likewise, the second
plurality of elongated
apertures has a second set of geometric characteristics and is arranged in a
second pattern. The
elongated apertures of the first plurality are orthogonally oriented with
respect to the elongated
apertures of the second plurality. Each of the elongated apertures is
obliquely angled with
respect to the top surface of the elastically rigid body. The geometric
characteristics and
pattern of the first plurality of elongated apertures are cooperatively
configured with the
geometric characteristics and pattern of the second plurality of elongated
apertures to provide a
desired or minimum cooling performance while exhibiting negative Poisson's
Ratio (NPR)
behavior under macroscopic planar loading conditions.
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[0011] Other aspects of the present disclosure are directed to methods of
manufacturing and
methods of using auxetic structures. In an example, a method is presented for
manufacturing
an auxetic structure. Said method includes: providing an elastically rigid
body with opposing
top and bottom surfaces; adding to the elastically rigid body a first
plurality of apertures
extending through the elastically rigid body from the top surface to the
bottom surface, the
first plurality of apertures being arranged in rows and columns; and, adding
to the elastically
rigid body a second plurality of apertures extending through the elastically
rigid body from
the top surface to the bottom surface, the second plurality of apertures being
arranged in rows
and columns. Each aperture of the first and/or second pluralities of elongated
apertures is
obliquely angled with the top surface of the elastically rigid body. The first
and second
pluralities of apertures are cooperatively configured to provide a desired or
minimum cooling
performance while exhibiting a negative Poisson's Ratio (NPR) behavior under
macroscopic
planar loading conditions. By way of example, the elongated apertures are
engineered with a
predefined porosity, a predetermined pattern, and/or a predetermined aspect
ratio to achieve
the desired NPR behavior. The auxetic structure may exhibit an effusion
cooling
effectiveness of approximately 30-50% and a Poisson's Ratio of approximately -
0.2 to -0.9%.
The elastically rigid body may take on various forms, such as a metallic sheet
or other
sufficiently elastic solid material.
[0012] The above summary is not intended to represent every embodiment or
every aspect of
the present disclosure. Rather, the foregoing summary merely provides an
exemplification of
some of the novel aspects and features set forth herein. The above features
and advantages,
and other features and advantages of the present disclosure, which are
considered to be
inventive singly or in any combination, will be readily apparent from the
following detailed
description of representative embodiments and modes for carrying out the
present invention
when taken in connection with the accompanying drawings and the appended
claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] FIG. 1 is a graph of Nominal Strain vs. Poisson's Ratio illustrating
the Poisson's Ratio
behavior of representative structures with elongated through holes according
to aspects of the
present disclosure.
[0014] FIGS. 2A-2C are illustrations of the representative structures of FIG.
1 corresponding
to specific data points from the graph.
[0015] FIGS. 3A and 3B are side-view and perspective-view illustrations,
respectively, of an
angled NPR S-slot according to aspects of the present disclosure.
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[0016] FIGS. 4A-4D are perspective-view illustrations of other angled NPR
slots in
accordance with aspects of the present disclosure.
[0017] FIGS. 5A and 5B are plan-view illustrations of an angled NPR S-slot and
an angled
NPR Z-slot, respectively, with variable cap rotation in accordance with
aspects of the present
disclosure.
[0018] FIGS. 6A-6D are plan-view illustrations of angled NPR S-slots
exhibiting a 0-degree
angle, a 45-degree angle, a 55-degree angle, and a 65-degree angle,
respectively, in
accordance with aspects of the present disclosure.
[0019] FIGS. 7A-7C are graphical illustrations of the cooling behaviors for
non-NPR normal
cooling holes, normal NPR cooling slots, and angled NPR cooling slots,
respectively, in
accordance with aspects of the present disclosure.
[0020] The present disclosure is susceptible to various modifications and
alternative forms,
and some representative embodiments have been shown by way of example in the
drawings
and will be described in detail herein. It should be understood, however, that
the inventive
aspects of this disclosure are not limited to the particular forms illustrated
in the drawings.
Rather, the disclosure is to cover all modifications, equivalents,
combinations and
subcombinations, and alternatives falling within the spirit and scope of the
invention as
defined by the appended claims.
DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS
[0021] This disclosure is susceptible of embodiment in many different forms.
There are
shown in the drawings, and will herein be described in detail, representative
embodiments
with the understanding that the present disclosure is to be considered as an
exemplification of
the principles of the present disclosure and is not intended to limit the
broad aspects of the
disclosure to the embodiments illustrated. To that extent, elements and
limitations that are
disclosed, for example, in the Abstract, Summary, and Detailed Description
sections, but not
explicitly set forth in the claims, should not be incorporated into the
claims, singly or
collectively, by implication, inference or otherwise. For purposes of the
present detailed
description, unless specifically disclaimed or logically prohibited: the
singular includes the
plural and vice versa; and the words "including" or "comprising" or "having"
means
"including without limitation." Moreover, words of approximation, such as
"about,"
"almost," "substantially," "approximately," and the like, can be used herein
in the sense of
"at, near, or nearly at," or "within 3-5% of," or "within acceptable
manufacturing tolerances,"
or any logical combination thereof, for example.
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[0022] Aspects of the present disclosure are directed towards auxetic
structures which
include repeating patterns of angled slots that provide negative Poisson's
Ratio (NPR)
behavior when macroscopically loaded. Poisson's Ratio (or "Poisson
coefficient") can be
generally typified as the ratio of transverse contraction strain to
longitudinal extension strain
in a stretched object. Poisson's Ratio is typically positive for most
materials, including many
alloys, polymers, polymer foams and cellular solids, which become thinner in
cross section
when stretched. The auxetic structures disclosed herein exhibit a negative
Poisson's Ratio
behavior.
[0023] According to aspects of the disclosed concepts, when an auxetic
structure is
compressed along one axis (e.g., in the Y-direction), coaxial strain results
in a moment
around the center of each cell because of the way the adjacent apertures are
arranged. This,
in turn, causes the cells to rotate. Each cell rotates in a direction opposite
to that of its
immediate neighbors. This rotation results in a reduction in the transverse
axis (X-direction)
distance between horizontally adjacent cells. In other words, compressing the
structure in the
Y-direction causes it to contract in the X-direction. Conversely, tension in
the Y-direction
results in expansion in the X-direction. At the scale of the entire structure,
this mimics the
behavior of an auxetic material. But many of the structures disclosed herein
are composed of
conventional materials. Thus, the unadulterated material itself may have a
positive Poisson's
Ratio, but by modifying the structure with the introduction of the angled-slot
patterns
disclosed herein, the structure behaves as having a negative Poisson's Ratio.
[0024] FIG. 1 is a graph of Poisson's Ratio (PR) against Nominal Strain
illustrating the
Poisson's Ratio behavior of three representative void structures shown in
FIGS. 2A-2C. The
chart of FIG. 1 shows the Poisson's Ratio of each test piece under load. At a
certain level of
deformation, the "instantaneous" PR can be determined and plotted against a
parameter (e.g.,
nominal strain) representing the level of deformation. When a designer has a
desired NPR
for an intended application, the level of deformation corresponding to that PR
can be
determined and the geometry of the holes at that condition determined. This
hole shape
pattern can then be machined (manufactured) on an unstressed part to achieve a
component
with the desired PR.
[0025] As seen in FIGS. 2B and 2C, the NPR aperture patterns can consist of
horizontally
and vertically oriented, elongated holes (also referred to as "apertures" or
"voids" or "slots"),
shown as elliptical through slots. These elongated holes are arranged on
horizontal and
vertical lines (e.g., rows and columns of a square array in FIG. 2B) in a way
that the vertical
lines are equally spaced and the horizontal in both dimensions lines are
equally spaced (also
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Ax=Ay). The center of each slot is on the crossing point of two of the lines.
Horizontally
oriented and vertically oriented slots alternate on the vertical and
horizontal lines such that
any vertically oriented slot is surrounded by horizontally oriented slots (and
vice versa),
while the next vertically oriented slots are found on both diagonals. These
voids can also act
as cooling and/or damping holes and, due to their arrangement, also as stress
reduction
features. One or more of the slots shown herein can be replaced by elongated
NPR
protrusions or semispherical NPR dimples.
[0026] Also disclosed are gas turbine combustors that are made with one or
more walls from a
material with any of the specific auxetic structure configurations disclosed
herein. In some
embodiments, the angled slots are generated in a metal body directly in a
stress-free state such
that the apertures are equivalent in shape to collapsed void shapes found in
rubber under
external load in order to get NPR behavior in the metal body without
collapsing the metallic
structure in manufacturing. Various manufacturing routes can be used to
replicate the void
patterns in the metallic component. The manufacturing does not necessarily
contain buckling
as one of the process steps. The auxetic structures disclosed herein are not
limited to the
combustor wall; rather, these features can be incorporated into other sections
of a turbine (e.g.,
a blade, a vane, etc.).
[0027] In a conventional combustor wall, holes used for cooling air flow and
damping also
act as stress risers. In some of the disclosed embodiments, as the wall
material at a hot spot
presses against its surrounding material, e.g., in a vertical direction, the
negative Poisson's
Ratio will make the wall material contract in the horizontal direction, and
vice versa. This
behavior will reduce the stresses at the hotspot significantly. This effect is
stronger than just
the impact of the reduced stiffness. Stress at hot spot gets reduced, for
example, by 50%
which, in turn, leads to an increase in stress fatigue life by several orders
of magnitude. The
stress reduction by the NPR behavior does not increase the air consumption of
the combustor
wall. The longer life could be used as such or the wall material could be
replaced by a
cheaper one in order to reduce raw material costs.
[0028] It has also been demonstrated that the replacement of circular
combustor cooling holes
with a fraction of elongated and angled air passages of 2-3% reduces thermo-
mechanical
stress by a factor of at least five, while maintaining the cooling and damping
performance.
For example, elliptical cooling holes in the combustor have been predicted to
result in a five-
fold decrease in the worst principal stress. Inducing NPR behavior, thus, adds
further
functionality to the cooling holes of the combustor in that the NPR behavior
generates a five-
fold reduction in worst principal stress as compared to traditional cooling
holes. In stress
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fatigue of a combustor-specific superalloy, halving the component stress
increases the fatigue
life by more than an order of magnitude. In some embodiments, the superalloy
may be a
nickel-based superalloy, such as Inconel (e.g. IN100, IN600, IN713), Waspaloy,
Rene alloys
(e.g. Rene 41, Rene 80, Rene 95, Rene N5), Haynes alloys, Incoloy, MP98T, TMS
alloys,
and CMSX (e.g. CMSX-4) single crystal alloys.
[0029] It has been shown that optimized porosity offers increased cooling
function. As used
herein, "porosity" can be defined to mean the surface area of the apertures,
AA, divided by
the surface area of the structure, AS, or Porosity = AA / AS. It may be
desirable, in some
embodiments, that the porosity of a given void structure be approximately 0.3-
9.0% or, in
some embodiments, approximately 1-4% or, in some embodiments, approximately
2%. By
comparison, many prior art arrangements require a porosity of 40-50%.
[0030] There may be a predetermined optimal aspect ratio for the elongated
apertures to
provide a desired NPR behavior. As used herein, "aspect ratio" of the
apertures can be
defined to mean the length divided by the width of the apertures, or the
length of the major
axis divided by the length of the minor axis of the apertures. It may be
desirable, in some
embodiments, that the aspect ratio of the apertures be approximately 5-40 or,
in some
embodiments, approximately 20-30. An optimal NPR may comprise, for example, a
PR of
about -0.2 to about -0.9 or, for some embodiments, about -0.5. Aspects of the
disclosed
concepts can be demonstrated on structural patterns created with a pattern
lengthscale at the
millimeter, and are equally applicable to structures possessing the same
periodic patterns at a
smaller lengthscale (e.g., micrometer, submicrometer, and nanometer
lengthscales) or larger
lengthscales so far as the unit cells fit in the structure.
[0031] Turning next to FIGS. 3-6, there are shown various examples of angled-
slot auxetic
structures which exhibit desired NPR behaviors and enhanced cooling
performance in
accordance with the present disclosure. FIGS. 3A and 3B, for example,
illustrate an auxetic
structure, designated generally at 300, which utilizes an alternating pattern
of elongated
asymmetrical slots. The foregoing slots are elongated in that each has a major
axis (e.g., a
length) that is larger than and perpendicular to a minor axis (e.g., a width).
As shown, the
auxetic structure 300 comprises an elastically rigid body 310, which may be in
the form of a
metallic sheet or other solid material with adequate elasticity to return
substantially or
completely to its original form once macroscopic loading conditions are
sufficiently reduced
or eliminated. Elastically rigid body 310 has a first (top) surface 314 in
opposing spaced
relation to a second (bottom) surface 316. Fabricated into the elastically
rigid body 310 is a
first plurality of S-shaped through slots (also referred to herein as
"apertures" or "voids" or
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"slots"), represented herein by slot 312, which extend through the body 310
from the top
surface 314 to the bottom surface 316. A
second plurality of S-shaped through
slots/apertures, represented herein by slots 318, also extends through the
elastically rigid
body 310 from the top surface 314 to the bottom surface 316. The pattern of
elongated
apertures present in the elastically rigid body 310 may be similar in
arrangement to what is
seen in FIGS. 2B and 2C.
[0032] S-shaped through slots 312, 318 are arranged in an array or matrix of
rows and
columns, with the first plurality of elongated apertures 312 extending
transversely with
respect to the second plurality of elongated apertures 318. Note that hidden
lines indicating
the internal structural configuration of slots 318 have been omitted from
FIGS. 3A and 3B for
clarity to better show the internal structural configuration of slots 312. For
at least some
embodiments, the rows are equally spaced from each other and, likewise, the
columns are
equally spaced from each other. According to the illustrated embodiment of
FIGS. 3A and
3B, for example, each row and each column comprises vertically oriented S-
shaped through
slots 312 interleaved with horizontally oriented S-shaped through slots 318.
In effect, each
vertically oriented through slot 312 is neighbored on four sides by
horizontally oriented
through slots 318, while each horizontally oriented through slot 318 is
neighbored on four
sides by vertically oriented through slots 312. With this arrangement, the
minor axes of the
first plurality of S-shaped through slots 312 are parallel to the rows of the
array, whereas the
minor axes of the second plurality of S-shaped through slots 318 are parallel
to the columns
of the array. Thus, the major axes of the through slots 318, which are
parallel to the rows of
the array, are perpendicular to the major axes of the through slots 312, which
are parallel to
the columns of the array. It is also envisioned that other patterns and
arrangements for
achieving stress reduction through NPR behavior are within the scope and
spirit of the
present disclosure.
[0033] The illustrated pattern of elongated, angled slots provides a specific
porosity (e.g., a
porosity of about 0.3 to about 9.0%) and a desired cooling performance (e.g.,
an effusion
cooling effectiveness of approximately 30-50%) while exhibiting a desired
negative
Poisson's Ratio behavior (e.g., a PR of about -0.2 to about -0.9) under
macroscopic planar
loading conditions (e.g., when tension or compression is applied in the plane
of the sheet).
When the auxetic structure 300 is stretched, for example via tensile force FT
along a vertical
axis Y, axial strain in the vertical direction results in a moment around the
center of each cell,
which causes the cells to rotate. A cell may consist of two laterally adjacent
vertical slots
aligned with two vertically adjacent horizontal slots to form a square-shaped
unit. Each cell
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rotates in a direction opposite to that of its immediate neighboring cells.
This rotation
increases the X-direction distance between horizontally adjacent cells such
that stretching the
structure in the Y-direction causes it to stretch in the X-direction. The
first plurality of S-
shaped through slots 312 have (first) engineered geometric characteristics,
including a
predefined geometry and a predefined aspect ratio, while the second plurality
of S-shaped
through slots 318 have (second) engineered geometric characteristics,
including a predefined
geometry and a predefined aspect ratio, that are cooperatively configured with
(third)
engineered geometric characteristics of the aperture pattern, including NPR-
slot density and
cell arrangement, to achieve a desired NPR behavior under macroscopic loading
conditions.
[0034] Each slot of the first and/or second pluralities of elongated S-shaped
through slots
312, 318 can be obliquely angled with respect to the top surface 314 or bottom
surface 316,
or both, of the auxetic structure's 300 elastically rigid body 310. In an
example, slot 312 is
shown in FIG. 3A traversing the entire thickness of the material at an angle
that is oblique to
the material's horizontal plane. For at least some embodiments, each aperture
has an angle 0
of approximately 20-80 degrees or, in some embodiments, approximately 40-70
degrees with
the top and bottom surfaces 314, 316 of the auxetic structure's body 310.
These
macroscopically patterned NPR voids ¨ S-shaped angled slots (FIGS. 3A, 3B, 4A
and 5A) or,
equivalently, I-shaped angled slots (FIG. 4B), barbell-shaped angled slots
(FIG. 4C),
elliptical angled slots (FIG. 4D), Z-shaped angled slots (FIG. 5B), C-shaped
angled slots, etc.
¨ serve as effusion cooling holes which allow a cooling fluid FL to traverse
one surface of the
auxetic structure, pass through the body at an inclination angle a, as shown
in FIG. 3A, and
traverse the opposing surface of the auxetic structure. This configuration
enhances film
cooling performance as compared to traditional cooling slots/holes that are
normal to the
thickness of the body and, thus, more restrictive of cooling fluid flow.
Inclination angle a
can be defined as the angle between the injection vector and its projection on
the material
plane. This inclination angle can be varied in a 360 rotational angle of
freedom to achieve
numerous desired combinations of auxetic behavior and film cooling
performance. Cooling
effectiveness (Eta) can be typified as a non-dimensional value that
quantitatively represents
how effectively a fluid flowing over a porous surface protects that surface
from a high
temperature mainstream flow. Cooling effectiveness can be defined as the
difference of the
hot gas temperature to the wall temperature in the presence of a cooling
device divided by the
difference of the hot gas temperature to the temperature of the supplied
cooling gas:
Eta=(T hotgas-T wall)/(T hotgas-T coolant).
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[0035] Patterned angled NPR-slot features, such as those disclosed in FIGS. 3-
6, have been
shown to cool significantly better than conventional right-angled (normal)
circular holes and
cooling slots as the internal surface area of the slots is larger than that of
normal circular
holes or slots. Adiabatic film cooling effectiveness is also increased
compared to traditional
normal cooling holes and slots, for example, due to a more even distribution
of cooling air
over the surface and reduced coolant jet penetration into the mainstream flow.
This can be
seen when comparing the cooling behaviors for representative non-NPR normal
cooling holes
(Eta = 17%), normal NPR cooling slots (Eta = 36%), and angled NPR S-slots (Eta
= 44%) of
FIGS. 7A, 7B and 7C, respectively. Angled NPR-slot film can benefit from the
Coanda
Effect, which causes the coolant jet to better adhere to the wall, rather than
lifting off and
penetrating the mainstream flow. This helps to decrease the inclination angle,
which in turn
decreases coolant jet penetration and increases cooling performance of NPR
slots. From an
aerodynamic perspective, the reduced penetration of the coolant jet of angled
NPR slots
decreases aerodynamic losses due to film cooling compared with normal coolant
slot flow.
The inclination angle can be varied to achieve a desired combination of
auxetic behavior and
film cooling performance.
[0036] It has been determined that having inclined cooling slots help to
provide better film
cooling effectiveness coverage in comparison to normal cooling holes with
internal walls that
are perpendicular to cooling flow. In addition, early investigation
demonstrates that coolant
ejection from an angled NPR slot is more efficient than ejection from normal
cooling holes
because the mixing process is less intensive for the closed film ejected from
the slot. While
the high thermal stresses encountered on gas turbine blades and vanes
typically do not allow
for the use of highly elongated slots, angled NPR slots help to reduce or
otherwise eliminate
high thermal stresses on turbine blades/vanes while enhancing film cooling
performance. For
at least some embodiments, it is generally desirable to minimize surface
porosity and the
amount of coolant used in a turbine engine; normal NPR slots can be replaced
with a smaller
number of angled NPR slots to minimize porosity. In this case, cooling flow
consumption
will be reduced while the film cooling performance of the effusion slots is
maintained.
[0037] As an exemplary implementation of the disclosed features, one can
consider a
combustor liner with sheet metal walls in which conventional round effusion
holes or normal
effusion slots are replaced with a pattern of angled S-shaped NPR slots
forming an auxetic
structure. Cooling air fed through these angled S-shaped slots removes heat
from the
structure and produces an even distribution of cooling air over the surface.
These angled
slots, which have an increased internal surface area, enhance film cooling
performance and
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improve mechanical response. Moreover, angled NPR slots are capable of
sustaining higher
flame temperatures, and help impart to the sheet a much longer life compared
to conventional
sheet metal walls with normal effusion holes.
[0038] Shown in FIGS. 4A-4D are perspective-view illustrations of other
auxetic structures,
designated generally at 400A, 400B, 400C and 400D, respectively, with angled
NPR slots in
accordance with aspects of the present disclosure. Although differing in
appearance, the
auxetic structures 400A-400D may include any of the features, options, and
alternatives
described herein with respect to the other auxetic structures. In the same
vein, unless
explicitly disclaimed or logically prohibited, any of the auxetic structures
disclosed herein
can share features, options and alternatives with the other disclosed
embodiments. Auxetic
structures 400A-400D each comprises an elastically rigid body 410A, 410B, 410C
and 410D,
respectively, fabricated with a plurality of elongated and angled apertures
412A, 412B, 412C
and 412D, respectively, arranged in a pattern to provide a desired cooling
performance while
exhibiting a predetermined NPR behavior under macroscopic planar loading
conditions. In
FIG. 4A, elongated apertures 412A have an S-shaped plan-view profile, whereas
the
elongated apertures 412B in FIG. 4B have an I-shaped plan-view profile, which
includes a
pair of spaced semicircular slots connected by an elongated linear slot. By
comparison,
elongated apertures 412D in FIG. 4D have an elliptical plan-view profile,
whereas the
elongated apertures 412C in FIG. 4C have a barbell-shaped plan-view profile,
which includes
a pair of spaced, rounded boreholes connected by an elongated linear slot. Any
of the
foregoing angled NPR slots can be manufactured by laser cutting, for example,
by laying out
a linear pattern of NPR slots along the inclination angle to the surface.
[0039] With continuing reference to FIGS. 4A-4D, the profile of the angled NPR
slots that
appears on the outer (top) surface can be designed as a projection of a
standard shape ¨ e.g., a
standard "S" 414A, a standard "I" 414B with rounded arms, a standard barbell
414C with
circular ends, and a standard ellipse 414D. Optionally, the profile of the
angled NPR slots
that appears on the outer (top) surface can be highly distorted from the
original image
depending, for example, on the desired angle and/or orientation of the slot.
FIGS. 6A-6D
illustrate slot distortion on an outer surface of a tubular auxetic structure:
FIG. 6A illustrating
normal NPR S-slots exhibiting a 0-degree angle; FIG. 6B illustrating angled
NPR S-slots
exhibiting a 45-degree angle; FIG. 6C illustrating angled NPR S-slots
exhibiting a 55-degree
angle; and FIG. 6D illustrating angled NPR S-slots exhibiting a 65-degree
angle.
[0040] A new NPR slot shape, for instance, Z-shaped slots 512A (FIG. 5A) and S-
shaped
slots (FIG. 5B), can be developed by reducing cap length 511A and 511B and/or
cap height
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513A and 513B to provide a horizontal projection similar to an existing or
"standard" S-
shape/Z-shape. The size and shape of the caps can be varied to achieve a
desired combination
of auxetic behavior and film cooling performance. Film cooling performance of
angled
effusion S-shaped slots or, equivalently, Z-shaped slots can be improved by
producing a
longer cooling thermal layer above the hot surface. A longer cooling thermal
layer can be
created by increasing the lateral area of the slots normal to the free
mainstream fluid by
rotating the S-shaped slot cap in the counter-clockwise direction (or
clockwise direction for
Z-shaped slot caps). This cap rotation angle 515A and 515B can be varied to
achieve a
desired combination of auxetic behavior and film cooling performance. By
rotating the caps
of the S-shaped slots in the counter-clockwise direction, the maximum
mechanical stress at
the top of the caps will be reduced and the film cooling performance of the
effusion slots will
be improved due to the increased coverage of the cooling thermal layer above
the hot surface.
[0041] Aspects of this disclosure are also directed to methods of
manufacturing and methods
of using auxetic structures. By way of example, a method is presented for
manufacturing an
auxetic structure, such as the auxetic structures described above with respect
to FIGS. 3-6.
The method includes, as an inclusive yet non-exclusive set of acts: providing
an elastically
rigid body, such as the elastically rigid body 310 of FIGS. 3A and 3B, with
opposing top and
bottom surfaces; adding to the elastically rigid body a first plurality of
apertures, such as the
elongated S-shaped slots 312 of FIGS. 3A and 3B, extending through the
elastically rigid
body from the top surface to the bottom surface; and, adding to the
elastically rigid body a
second plurality of apertures, such as the elongated S-shaped slots 318 of
FIGS. 3A and 3B,
extending through the elastically rigid body from the top surface to the
bottom surface. The
first and second pluralities of apertures are arranged in rows and columns.
Each aperture of
the first and/or second plurality is obliquely angled with the top surface of
the elastically rigid
body. The first and second pluralities of apertures are cooperatively
configured to provide a
predefined cooling performance while exhibiting a predetermined negative
Poisson's Ratio
(NPR) behavior under macroscopic planar loading conditions. By way of example,
the
elongated apertures are engineered with a predefined porosity, a predetermined
pattern,
and/or a predetermined aspect ratio to achieve the desired NPR behavior. The
auxetic
structure may exhibit an effusion cooling effectiveness of approximately 30-
50% and a
Poisson's Ratio of approximately -0.2 to -0.9%. The elastically rigid body may
take on
various forms, such as a metallic sheet or other sufficiently elastic solid
material.
[0042] In some embodiments, the method includes at least those steps
enumerated above and
illustrated in the drawings. It is also within the scope and spirit of the
present invention to
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omit steps, include additional steps, and/or modify the order presented above.
It should be
further noted that the foregoing method can be representative of a single
sequence for
designing and fabricating an auxetic structure. However, it is expected that
the method will
be practiced in a systematic and repetitive manner.
[0043] The present invention is not limited to the precise construction and
compositions
disclosed herein. Rather, any and all modifications, changes, combinations,
permutations and
variations apparent from the foregoing descriptions are within the scope and
spirit of the
invention as defined in the appended claims. Moreover, the present concepts
expressly
include any and all combinations and subcombinations of the preceding elements
and aspects.
